O is a point inside a rectangle ABCD such that OB = 6 cm, OD = 8 cm and OA = 5 cm. Find OC.

In △ABC, ∠ABC = 90°, AB = 6 cm, BC = 8 cm. Find the circum-radius of triangle ABC.

In a triangle PQR, ∠P = 90° and PS is perpendicular to QR. Then prove that

Use graph paper, taking 2 cm = 1 unit along both axes. (a) Plot A(1, 3), B(1, 2) and C(3, 0). (b) Reflect A and B in the x-axis and name their images E and D. Write their coordinates. (c) Reflect A and B through the origin and name their images F and G. (d) Reflect A, B and C in the y-axis and name their images J, I and H. (e) Join A, B, C, D, E, F, G, H, I and J in order and name the closed figure.

In the given diagram, O is the centre of the circle. Chord SR produced meets the tangent XTP at P. (a) Prove that △PTR ∼ △PST. (b) Prove that PT² = PR × PS. (c) If PR = 4 cm and PS = 16 cm, find the length of tangent PT.

Refer to the bill below. A customer paid ₹2,000, rounded to the nearest ₹10, to clear it. Note: A 5% discount applies to an article when 10 or more units are purchased. Article Marked price Quantity GST A ₹190 6 12% B ₹50 12 18% Check whether the amount paid is correct. Justify your answer with working.

In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is: (a) 30° (b) 60° (c) 90° (d) 120°

If 1701 is the nth term of the Geometric Progression 7, 21, 63, …, find: (a) the value of n. (b) hence, the sum of the n terms of the G.P.

It is given that (x − 2) is a factor of 2x³ − 7x² + kx − 2. (a) Find k. (b) Hence, factorise the resulting polynomial completely.

Using ruler and compass, construct △ABC where AB = 6 cm, AC = 4.5 cm and ∠BAC = 120°. Construct the circle circumscribing △ABC. Measure and write the radius of the circle.

Solve the quadratic equation 2x² − 5x − 4 = 0. Give your answers correct to three significant figures.

The factor common to the two polynomials x² − 4 and x³ − x² − 4x + 4 is: (a) (x + 1) (b) (x − 1) (c) (x − 2) (d) (x − 4)